Similarly, general relativistic spacetimes may allow for closed timelike curves (as for instance within the Kerr-Newman solution, describing spacetime around a rotating charged mass), which create difficulties for the very notion of `production' at the heart of the non-Humean nature of the primitivist and dispositionalist conceptions of laws. [1]} is very explicit about the fact that closed timelike curves would undermine the sort of productive explanation of the Humean mosaic that (his version of) primitivism about laws provides: “Production is clearly transitive, so production-in-a-circle would imply self-production, but an item cannot be the ontological ground of its own production. This means that the existence of closed timelike curves would imply the non-existence of this sort of productive explanation, and might suggest that a Humean account is the strongest that can be had.” What is interesting for us here is that this stance further underlines central features of the non-Humean strategy at work in the primitivist and dispostionalist conceptions: that is, to consider a (proper) subset of all the occurrent facts (i.e. a subset of the Humean mosaic) as the ontological ground for the rest of the totality of occurrent facts (i.e. for the whole Humean mosaic), the latter then being produced and therefore productively explained by the former. This strategy is explicitly non-Humean in that it encodes some primitive modality—in the primitive laws or in the irreducible dispositions—as well as some form of necessity—between the ontological ground and what is derived from it. As we will see in the next section (§REF ), one way for the primitivist and dispositionalist conceptions of laws to face the challenge that arises in the context of quantum gravity is to articulate and generalize this non-Humean strategy in a way that does not rely on spacetime and on spatiotemporal notions.
